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| HAL: hal-00658665, version 1 |
| arXiv: 1201.2162 |
| Detailed view |  Export this paper |
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| International Mathematics Research Notices (2012) 10.1093/imrn/rns119 |
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| The Euclidean Onofri inequality in higher dimensions |
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| Manuel Del Pino 1Jean Dolbeault 2 |
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| (2012-12-31) |
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| The classical Onofri inequality in the two-dimensional sphere assumes a natural form in the plane when transformed via stereographic projection. We establish an optimal version of a generalization of this inequality in the d-dimensional Euclidean space for any d≥2, by considering the endpoint of a family of optimal Gagliardo-Nirenberg interpolation inequalities. Unlike the two-dimensional case, this extension involves a rather unexpected Sobolev-Orlicz norm, as well as a probability measure no longer related to stereographic projection. |
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| 1: | Departamento de Ingeniería Matemática [Santiago] (DIM) |
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Departamento de Ingeniería Matemática – Universidad de Chile |
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| 2: | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| Subject | : | Mathematics/Analysis of PDEs |
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| Sobolev inequality – logarithmic Sobolev inequality – Onofri inequalities – Gagliardo-Nirenberg inequalities – interpolation – extremal functions – optimal constants – stereographic projection |
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| hal-00658665, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00658665 | |
| oai:hal.archives-ouvertes.fr:hal-00658665 | |
| From: Jean Dolbeault | |
| Submitted on: Tuesday, 10 January 2012 19:43:20 | |
| Updated on: Wednesday, 5 December 2012 19:23:37 | |
